Brian's dog ran away, no one has been able to find him yet?

You could use a semicolon.

Brian's dog ran away; no one has been able to find him.

Two closely related clauses are linked in this case. With a semicolon it's easy to see that both sentences refer to Brian's dog. When you separate the two by a period you should refer specifically back to the dog from the first sentence or it could be misconstrued as Brian whom no one is able to find.

Alternatively, you could use an article to link the two.

Brian's dog ran away, and no one has been able to find him.